The debt ceiling crisis barely was averted Tuesday when President Barack Obama and other top Democrats were ready to change the subject.

Obama offered little praise for the $2.1 trillion deficit package during a press conference at the Rose Garden, instead vowing to fight for “new jobs, higher wages and faster economic growth” in the coming months — an agenda he has tried to resurrect at least a half-dozen times in the past two years.

Democrats on Capitol Hill are backing up Obama, hoping to take up various proposals dropped from the debt ceiling compromise or sidetracked by the winding debate, such as approving trade deals, extending the payroll tax cut and unemployment insurance, and allocating funding for new highway infrastructure and a clean energy program.

“There’s no reason for Congress not to send me those bills so I can sign them into law right away, as soon as they get back from recess,” Obama said. “Both parties share power in Washington, and both parties need to take responsibility for improving this economy. It’s not a Democratic responsibility or a Republican responsibility, it is our collective responsibility as Americans. And I’ll be discussing additional ideas in the weeks ahead to help companies hire, invest and expand.”

Although Democrats say they are eager to pick up the jobs torch, even supporters admit it is going to be a tough sell. Republicans, who rode to victory last year criticizing the president’s stimulus package and have forced deep cuts in government spending this year, appear ready to keep up their efforts in the coming spending battles.

“I understand we want to get back to jobs, we should get back to jobs, but these government fiscal questions are going to be with us every step of the way from here until the end of 2012,” said Sen. Joe Lieberman, a Connecticut independent who caucuses with Democrats.

In the Senate, Democrats plan to focus on a jobs proposal authored by Sen. Chuck Schumer (D-N.Y.) that calls for a variety of tax cuts and credits, funding for new highway infrastructure, a clean energy program, immigration reform for highly skilled workers to spur innovation and new technology and a bill to restrict currency manipulation by China. Schumer teased the proposal in June, but it was overtaken by the debt ceiling negotiations this summer.

Flanked by his top lieutenants, Senate Majority Leader Harry Reid (D-Nev.) told reporters that Congress’s No. 1 job was “creating jobs for the American people.” Added Schumer: “It’s now time for Congress to get back to our regularly scheduled programming, and that means jobs.”

And across the Capitol, House Minority Leader Nancy Pelosi (D-Calif.) sidestepped questions about who she’d name to a new deficit committee, saying: “It’s time for us to completely focus on jobs. So I have no intention for the next weeks and months to be talking about this committee.”

When Congress returns after Labor Day, it will have to take on two major spending questions: the budget for the next fiscal year and a package worth about $1.5 trillion in deficit reduction, yet to be designed by a 12-member super committee. If the committee’s cuts aren’t passed before Christmas, Medicare and the Pentagon would be dealt serious blows.

Conservatives will take both fights seriously. Those who fought tooth and nail for the debt-limit hike to be tied to trillions in cuts over the next decade — while rejecting Democrats’ insistence on fresh tax revenues — say they’ve barely scratched the surface in slashing the deficit.

“We certainly didn’t fix the problem here. That’s disappointing,” Sen. Ron Johnson (R-Wis.), a tea-party-backed freshman, told POLITICO after voting against the debt hike Tuesday. “We’re still increasing our debt by an enormous amount. … We’ve got to start actually honestly looking at what the situation is in this country and start addressing it. This just isn’t enough and that’s unfortunate.”

But to Obama’s progressive critics, the Democrats’ pivot from a deficit-driven message is long overdue.

“I think he has to stop talking about the deficit,” said Andy Stern, a former Service Employees International Union president and longtime Obama ally. “People want to talk about jobs. He needs to stop simply talking jets and corporate tax breaks — only as they pertain to jobs — and he needs to put out his own plan. Why can’t he and Harry Reid put out a bill that says we’re going to close these loopholes and pay for a summer job for every kid this summer? If the Republicans want to filibuster, fine, keep the floor open for two weeks and do nothing but debate jobs.”

Stern, echoing the sentiments of some economists, predicts the national unemployment rate is likely to rise as a result of the federal budget cuts as they are passed down to state and local governments, and thinks local property taxes might have to be raised to stanch a new wave of teacher, firefighter and police layoffs.

“People are looking for jobs. Anything beyond that message at this point is wasted energy.”

Another top Obama ally in labor, American Federation of Teachers President Randi Weingarten, thinks the president needs to make it much clearer that he regards government jobs as a vital part of the recovery and let his base know he’s willing to fight conservatives, like Wisconsin Gov. Scott Walker, who are attacking collective-bargaining rights.

“Given the timing and the intervention of the rating agencies, it was clear the president needed to do this to avoid default, but we have a jobs crisis and demand crisis the likes of which we haven’t seen since the 1930s,” she said.

“It feels like there’s a real disconnect between what needs to be done and what’s being done. … So I think he needs to put a spotlight on how cuts to education, which are coming, are bad, not good — and that disinvestment in states and cities is going to cost jobs.”

Obama met Tuesday morning with the AFL-CIO executive committee, a group of professional bargainers frustrated by the lopsided nature of the debt deal and the lack of focus in recent months on jobs.

The president told the labor leaders that he tried the best he could, promising to be tougher next time and turn his full attention to jobs, according to a union source briefed on the meeting. Obama did receive praise for protecting Medicaid.

After a month confined in Washington for the debt negotiations, Obama plans to hit the road over the next two weeks to promote elements of his agenda that didn’t make it into the package: job-creation measures and a “balanced” approach to tax reform.

He will continue to talk about deficit reduction, but only as one component of a larger economic message focused on jobs, administration officials said.

“I would be shocked if he spent significant resources reminding people of this bill because it would remind people of the spectacle of the last three months and everything they hate about Washington,” said Neera Tanden, a former Obama administration aide and chief operating officer of the Center for American Progress, a liberal policy organization.